设集合A={x|-1≤X≤a,a>-1},B={y|y=X+1,x∈A},C=y|y=X눀,x∈A},若B=C,求a的值

2025-06-20 11:38:21
推荐回答(2个)
回答1:

A={x|-1≤X≤a,a>-1},
B={y|y=X+1,x∈A}=[0,a+1],
C=y|y=X²,x∈A}
={[a^2,1](-1{[0,1](0<=a<=1),
{[0,a^2](a>1).
由B=C得a+1=1(0<=a<=1),或a+1=a^2(a>1),
解得a=0,或a=(1+√5)/2.

回答2:

因为B=C
所以 y=X+1=X², x∈A
解得 x=(1+√3)/2 或x=(1-√3)/2
又 x∈A
则a≧(1+√3)/2